Heat transfer from a buried pipe carrying a flowing liquid is analysed using a 3-dimensional geometry, transient modelling and numerical methods. The pipe is buried horizontally in soil whose initial surface temperature is assumed to be below that of the bulk soil and the pipe, and also below the freezing temperature of the liquid. The problem is solved using string-intersected-boundaries and a three-level alternating-direction-implicit finite-difference method. It is possible to predict the time taken for the fluid anywhere in the pipe to fall to its freezing point. The minimum burial depth needed so that the pipe does not freeze is also predicted. The simulation was run on an ordinary mainframe computer with very small computation times. The package developed can be used by designers such as pipeline, plant and water distribution engineers.